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This is then multiplied on both sides by [H ]. In the first term we can reexpress the derivative in .NET Add ECC200 in .NET This is then multiplied on both sides by [H ]. In the first term we can reexpress the derivative




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This is then multiplied on both sides by [H ]. In the first term we can reexpress the derivative generate, create data matrix ecc200 none on .net projects BIRT Reporting Tools H qm qm qm Visual Studio .NET DataMatrix qpH q H q log H (12:34). Dividing Eq. (12.3 3) through by the sum on the left leaves the first term on the right as m2 and the second term as m2 .

With the aid of Eq. (12.1) we have an expression for the fluctuations in m.

12.7 F L U C T U A T I O N S I N A T W O - S T A T E S Y S T E M qm m2 m2 m2 qpH (12:35). Thus, a protein s charge will fluctuate the most at a pH where the titration curve is steepest. This usually occurs near the isoelectric point. Equation (12.

35) was used to estimate the fluctuations in charge of hemoglobin, giving an rms charge at the isoelectric point of about 1.85 (Cohn and Edsall, 1943). For ribonuclease a value of 3.

65 was obtained (Tanford, 1961, p. 573)..

12.7 Fluctuations in a two-state system The two-state mode l was examined in earlier chapters to understand protein conformational transitions (Scheme (12B)). ! A B (12B). At equilibrium we have B K eq A (12:36). The equilibrium co nstant can also be expressed in terms of the rate constants as Keq / (Section 7.3). If the total protein concentration is T, with [A] [B] T, then at equilibrium the number of molecules of B and A will be fractions of T.

Replacing Keq in Eq. (12.36) with / and rearranging gives.

A T (12:37a). B T (12:37b). Note that [A] and [B] in these two expressions are actually average concentrations. At any instant in time there will be fluctuations as small excesses of A or B appear. These fluctuations dissipate and reappear as a result of the stochastic behavior arising from the independent conformational transitions of each protein.

We will first evaluate the magnitude of these fluctuations, and then in Section 12.9 we will examine their dynamics. From Eqs.

(12.37a) and (12.37b) we write the equilibrium probability of a protein molecule being in conformation A or B as.

pa (12:38a). pb (12:38b). FLUCTUATIONS Since each protein Data Matrix barcode for .NET molecule is independent, we can use the binomial distribution to express the probabilities of finding a certain number of molecules in one conformation or the other. Take Nt as the total number of protein molecules.

The probability of finding Na molecules in conformation A is. P N a Nt! p N a 1 pa N t N a N a ! N t N a ! a (12:39). A corresponding ex Visual Studio .NET Data Matrix 2d barcode pression can be written for P(Nb). The situation is now mathematically equivalent to the random walk of 6, where the binomial distribution was used to calculate the probability of a particular number of steps to the right or left.

We can thus use Eq. (6.37) to obtain the mean number of molecules of A or B.

This analysis leads back to Eqs. (12.37a) and (12.

37b). For A we have. Na Nt X Na 0 Nt! p N a 1 p a N t N a N t pa N t N a ! N t N a ! a (12:40). where Eq. (12.38a) 2d Data Matrix barcode for .

NET was used to replace pa. For the fluctuations we need to know the mean square as well, so we use Eq. (6.

42) to give. N a2 Nt X Na 0 N a2 Nt! p N a 1 pa VS .NET Data Matrix barcode N t N a N t pa 2 N t pa 1 pa N a ! N t N a ! a (12:41). Combining Eqs. (12 .40) and (12.

41) gives the fluctuations in number of molecules of A around the mean. N a2 N a2 N a N t pa 1 pa N t 2. (12:42). Once again we see that the mean-square fluctuations scale as N. Thus, the rms fluctuations, as a fraction of the average number of molecules of A can be expressed as. q N a barcode data matrix for .NET 2 Na r N p (12:43). and the fluctuations relative to the mean decrease with size, scaling as N . 12.8 Single-channel current Fluctuation analys is has been used to study ion channels. As ion channels open and close the current through the cell membrane fluctuates. Analysis of these fluctuations provided some of the first estimates of unitary channel properties.

Although this method has.
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